Kiran Dandekar
Balasundar I. Raju
Mandayam A. Srinivasan*
The Touch Lab
Department of Mechanical Engineering, and
The Research Laboratory of Electronics
Massachusetts Institute of Technology
Cambridge, MA 02139
3-D Finite-Element Models of
Human and Monkey Fingertips to
Investigate the Mechanics of
Tactile Sense
The biomechanics of skin and underlying tissues plays a fundamental role in the human
sense of touch. It governs the mechanics of contact between the skin and an object, the
transmission of the mechanical signals through the skin, and their transduction into
neural signals by the mechanoreceptors. To better understand the mechanics of touch, it
is necessary to establish quantitative relationships between the loads imposed on the skin
by an object, the state of stresses/strains at mechanoreceptor locations, and the resulting
neural response. Towards this goal, 3-D finite-element models of human and monkey
fingertips with realistic external geometries were developed. By computing fingertip model
deformations under line loads, it was shown that a multi-layered model was necessary to
match previously obtained in vivo data on skin surface displacements. An optimal ratio of
elastic moduli of the layers was determined through numerical experiments whose results
were matched with empirical data. Numerical values of the elastic moduli of the skin
layers were obtained by matching computed results with empirically determined force-
displacement relationships for a variety of indentors. Finally, as an example of the rel-
evance of the model to the study of tactile neural response, the multilayered 3-D finite-
element model was shown to be able to predict the responses of the slowly adapting type
I (SA-I) mechanoreceptors to indentations by complex object shapes.
DOI: 10.1115/1.1613673
1 Introduction
Just as the optics of the eye and acoustics of the ear are funda-
mental to understand our senses of vision and hearing, the me-
chanics of the skin is important to understand our sense of touch.
When an object is explored and manipulated with the hand, the
peripheral neural signals received and used by the brain to infer
the properties of the object in contact with the fingertips are the
trains of neural impulses generated by the population of mechan-
oreceptors embedded in the skin. These spatially distributed
mechanoreceptors transduce the mechanical state stresses,
strains, or a combination in their respective neighborhoods and
generate the neural impulses. However, the mechanical state at
receptor locations is not empirically observable with the current
technology. Therefore, there is a need for the development of
reliable models of the fingertip to investigate the mechanistic
bases of touch.
The structure as well as the material behavior of the primate
fingertip is complex, owing to irregularly shaped layers of tissues
that exhibit nonlinear force-displacement relations, anisotropy,
rate and time dependence. Lanir 1 has compiled various forms
of constitutive models for skin approximately 25 in number and
it is unlikely that a common agreement will emerge in the near
future. Also most of the available material data are from tension
tests on excised specimens, the properties of which are known to
be different from that of in vivo tissues due to the loss of natural
tension, absence of blood flow, and specimen preparation effects.
Moreover, no reliable data exists on the geometry and material
properties of individual layers of tissues that make up the finger-
pad. Therefore, our approach is a combination of mechanics and
systems modeling, which treats the fingertip as a black box to
develop reduced order mechanistic models whose input-output re-
lationship matches the corresponding biomechanical data 2. The
number of model parameters whose values are altered to achieve
the match are kept to a minimum. This is consistent with our view
that a model need not and should not incorporate complexities
unless it is forced to do so.
We first developed the ‘‘waterbed’’model, which idealized the
fingertip as an elastic membrane representing the skin enclosing
an incompressible fluid representing the subcutaneous tissues 3.
Although the model accurately predicted in vivo measurements of
skin surface deflection profiles under line loads, it failed to predict
the observed spatial distribution of mechanoreceptor responses. In
contrast, a sequence of 2-D plane strain models composed of a
homogeneous linear elastic material failed to predict the deflection
profiles under line loads, but matched the spatial response profiles
of SA-I mechanoreceptors under rectangular gratings very well
2,4,5. From these studies, we concluded that model geometry is
important in predicting mechanoreceptor responses. Further, to
match both the surface deflection and mechanoreceptor response
profiles, we hypothesized that a thick elastic layer with embedded
receptors and supported by an incompressible fluid or a soft solid
is needed 2.
Subsequently, several researchers have attempted to model the
mechanical aspects of the fingerpad. Serina et al. 6 modeled the
finger as an inflated ellipsoidal membrane for the epidermis filled
with an incompressible fluid modeling the subcutaneous fat,
which is similar to our earlier waterbed model 3. Although this
model accounted for empirical data described in 7, its formula-
tion limits it to loading by flat-plate indentors. Maeno et al. 8,9
developed a two-dimensional inhomogeneous finite element
model of the fingerpad, but no empirical verifications of the capa-
bilities of the model were done, and the elastic constants were
determined using a single cadaver tissue. Pawluk and Howe 10
used a lumped parameter model for predicting the dynamic force-
displacement response of the finger, but the model is incapable of
determining the spatial distribution of surface pressure, or the dis-
tribution of the mechanical stresses and strains in the vicinity of
the mechanoreceptors.
*Corresponding address: Massachusetts Institute of Technology, Room 36-791,
50 Vassar Street, Cambridge MA 02139; Phone: 617-253-2512; Fax: 617-258-7003;
e-mail: srini@mit.edu.
Contributed by the Bioengineering Division for publication in the JOURNAL OF
BIOMECHANICAL ENGINEERING. Manuscript received by the Bioengineering Divi-
sion July 11, 2002; revision received April 28, 2003. Associate Editor: C. R. Jacobs.
682 Õ Vol. 125, OCTOBER 2003 Copyright © 2003 by ASME Transactions of the ASME